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Standard deviation

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Ken Plummer
Ken Plummer

The document discusses the conceptual definition of standard deviation. Standard deviation represents the root average of the squared deviations of scores from the mean. It explains that to calculate standard deviation, each score's deviation from the mean is squared, those squared deviations are averaged, and then the square root of the average is taken to determine the standard deviation in the original units of measurement.

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Standard Deviation Conceptual Explanation Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. So, what does this mean? Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. Letโ€™s see an example: Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 Here is a distribution of scores Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 The mean of this distribution is 5 Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 And this observation is 9 Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 So we subtract this observation โ€œ9โ€ from the mean โ€œ5โ€ and we get +4 Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This means that this observation is +4 units from the mean. Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 And this observation is +3 units from the mean. Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 And this observation is +2 units from the mean. Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 And this observation is +1 unit from the mean. Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This observation is +1 unit from the mean. Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 And this observation is +2 units from the mean. Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 And this observation is +1 unit from the mean. Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 These values are all 0 units from the mean Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This observation is -1 unit from the mean. Standard Deviation`
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This observation is -1 unit from the mean. Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This observation is -1 unit from the mean. Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This observation is -2 units from the mean. Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This observation is -2 units from the mean. Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This observation is -3 units from the mean. Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This observation is -4 units from the mean. Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 Some might think all we need to do now is take the average of all of these values and weโ€™ll get the average deviation. Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 Some might think all we need to do now is take the average of all of these values and weโ€™ll get the average deviation. Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 But, because half of the deviations are positive and the other half are negative, if you take the average it will come to zero Standard Deviation
So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 Standard Deviation
So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 Standard Deviation
So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations 2 134 So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations 4 units below the mean Standard Deviation
So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations 1 So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations 1 unit below the mean Standard Deviation
So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations 1 2 So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations 2 units above the mean Standard Deviation
So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations 1 2 3 4 So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations 4 units above the mean Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This gives us the average squared deviation (or distance) of all the scores from the mean, which in this case letโ€™s say is 9. This is called the variance and will be discussed later. Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This gives us the average squared deviation (or distance) of all the scores from the mean, which in this case letโ€™s say is 9. This is called the variance and will be discussed later. Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 To get the average deviation (or distance) from the mean we just take the square root of the average squared deviation from the mean. The square root of 9 would be 3. Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 To get the average deviation (or distance) from the mean we just take the square root of the average squared deviation from the mean. The square root of 9 would be 3. Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 By taking the square root of the variance we are putting the value back into the original unit of measurement. If the original unit of measurement were INCHES then the standard deviation would be 3 INCHES Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 By taking the square root of the variance we are putting the value back into the original unit of measurement. If the original unit of measurement were INCHES then the standard deviation would be 3 INCHES Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 By taking the square root of the variance we are putting the value back into the original unit of measurement. If the original unit of measurement were DECIBELS then the standard deviation would be 3 DECIBELS
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 By taking the square root of the variance we are putting the value back into the original unit of measurement. If the original unit of measurement were DECIBELS then the standard deviation would be 3 DECIBELS Standard Deviation
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 By taking the square root of the variance we are putting the value back into the original unit of measurement. If the original unit of measurement were HOCKEY STICKS then the standard deviation would be 3 HOCKEY STICKS
Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 By taking the square root of the variance we are putting the value back into the original unit of measurement. If the original unit of measurement were HOCKEY STICKS then the standard deviation would be 3 HOCKEY STICKS Standard Deviation
Standard Deviation The standard Deviation is used in many statistical formulas and analyses.
Standard Deviation The standard Deviation is used in many statistical formulas and analyses. Here is the formula: Standard Deviation
Standard Deviation The standard Deviation is used in many statistical formulas and analyses. Here is the formula: Standard Deviation
Standard Deviation Standard Deviation
Standard Deviation Person Score A 1 B 4 C 7 Standard Deviation
Standard Deviation Person Score A 1 B 4 C 7 Standard Deviation
Standard Deviation Person Score A 1 B 4 C 7 Standard Deviation
Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Standard Deviation
Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Standard Deviation
Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Standard Deviation
Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Standard Deviation
Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9
Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Standard Deviation
Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Standard Deviation
Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Standard Deviation
Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Standard Deviation
Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Square Root 2.4 Standard Deviation
Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Square Root 2.4 Standard Deviation
Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Square Root 2.4 This is the Standard Deviation Standard Deviation
Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Square Root 2.4 So, technically, the standard deviation is the root average squared deviation from the mean. Standard Deviation
Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Square Root 2.4 So, technically, the standard deviation is the root average squared deviation from the mean. Standard Deviation
Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Square Root 2.4 So, technically, the standard deviation is the root average squared deviation from the mean. Standard Deviation
Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Square Root 2.4 So, technically, the standard deviation is the root average squared deviation from the mean. Standard Deviation
Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Square Root 2.4 So, technically, the standard deviation is the root average squared deviation from the mean. Standard Deviation
Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Square Root 2.4 So, technically, the standard deviation is the root average squared deviation from the mean. Standard Deviation
Standard Deviation The standard deviation has many uses. Standard Deviation
Standard Deviation The standard deviation has many uses. First and foremost it is a number that describes how scores in a distribution are spread out from one another. Standard Deviation
Standard Deviation The standard deviation has many uses. First and foremost it is a number that describes how scores in a distribution are spread out from one another. Standard Deviation = 2 Standard Deviation
Standard Deviation The standard deviation has many uses. First and foremost it is a number that describes how scores in a distribution are spread out from one another. Standard Deviation = 2 Standard Deviation = 18 Standard Deviation
Standard Deviation The standard deviation has many uses. First and foremost it is a number that describes how scores in a distribution are spread out from one another. Standard Deviation = 2 Standard Deviation = 18 What do you think a distribution with a standard deviation of 1 might look like? Standard Deviation
Standard Deviation The standard deviation has many uses. First and foremost it is a number that describes how scores in a distribution are spread out from one another. Standard Deviation = 2 Standard Deviation = 18 What about standard deviations of 10 or 20? Standard Deviation
The End Standard Deviation

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Standard deviation

  • 2. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. Standard Deviation
  • 3. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. So, what does this mean? Standard Deviation
  • 4. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. Letโ€™s see an example: Standard Deviation
  • 5. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 Here is a distribution of scores Standard Deviation
  • 6. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 The mean of this distribution is 5 Standard Deviation
  • 7. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 And this observation is 9 Standard Deviation
  • 8. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 So we subtract this observation โ€œ9โ€ from the mean โ€œ5โ€ and we get +4 Standard Deviation
  • 9. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This means that this observation is +4 units from the mean. Standard Deviation
  • 10. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 And this observation is +3 units from the mean. Standard Deviation
  • 11. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 And this observation is +2 units from the mean. Standard Deviation
  • 12. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 And this observation is +1 unit from the mean. Standard Deviation
  • 13. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This observation is +1 unit from the mean. Standard Deviation
  • 14. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 And this observation is +2 units from the mean. Standard Deviation
  • 15. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 And this observation is +1 unit from the mean. Standard Deviation
  • 16. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 These values are all 0 units from the mean Standard Deviation
  • 17. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This observation is -1 unit from the mean. Standard Deviation`
  • 18. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This observation is -1 unit from the mean. Standard Deviation
  • 19. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This observation is -1 unit from the mean. Standard Deviation
  • 20. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This observation is -2 units from the mean. Standard Deviation
  • 21. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This observation is -2 units from the mean. Standard Deviation
  • 22. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This observation is -3 units from the mean. Standard Deviation
  • 23. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This observation is -4 units from the mean. Standard Deviation
  • 24. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 Some might think all we need to do now is take the average of all of these values and weโ€™ll get the average deviation. Standard Deviation
  • 25. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 Some might think all we need to do now is take the average of all of these values and weโ€™ll get the average deviation. Standard Deviation
  • 26. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 But, because half of the deviations are positive and the other half are negative, if you take the average it will come to zero Standard Deviation
  • 27. So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 Standard Deviation
  • 28. So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 Standard Deviation
  • 29. So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations 2 134 So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations 4 units below the mean Standard Deviation
  • 30. So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations 1 So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations 1 unit below the mean Standard Deviation
  • 31. So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations 1 2 So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations 2 units above the mean Standard Deviation
  • 32. So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations 1 2 3 4 So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations So to avoid this happening, we square each deviation (-42 = 16, -12 = 1, 22 = 4, 42 = 16). Then we add up all of the squared deviations and divide that number by the number of observations 4 units above the mean Standard Deviation
  • 33. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This gives us the average squared deviation (or distance) of all the scores from the mean, which in this case letโ€™s say is 9. This is called the variance and will be discussed later. Standard Deviation
  • 34. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 This gives us the average squared deviation (or distance) of all the scores from the mean, which in this case letโ€™s say is 9. This is called the variance and will be discussed later. Standard Deviation
  • 35. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 To get the average deviation (or distance) from the mean we just take the square root of the average squared deviation from the mean. The square root of 9 would be 3. Standard Deviation
  • 36. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 To get the average deviation (or distance) from the mean we just take the square root of the average squared deviation from the mean. The square root of 9 would be 3. Standard Deviation
  • 37. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 By taking the square root of the variance we are putting the value back into the original unit of measurement. If the original unit of measurement were INCHES then the standard deviation would be 3 INCHES Standard Deviation
  • 38. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 By taking the square root of the variance we are putting the value back into the original unit of measurement. If the original unit of measurement were INCHES then the standard deviation would be 3 INCHES Standard Deviation
  • 39. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 By taking the square root of the variance we are putting the value back into the original unit of measurement. If the original unit of measurement were DECIBELS then the standard deviation would be 3 DECIBELS
  • 40. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 By taking the square root of the variance we are putting the value back into the original unit of measurement. If the original unit of measurement were DECIBELS then the standard deviation would be 3 DECIBELS Standard Deviation
  • 41. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 By taking the square root of the variance we are putting the value back into the original unit of measurement. If the original unit of measurement were HOCKEY STICKS then the standard deviation would be 3 HOCKEY STICKS
  • 42. Standard Deviation Conceptually, the standard deviation represents the root average squared deviations of scores from the mean. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 By taking the square root of the variance we are putting the value back into the original unit of measurement. If the original unit of measurement were HOCKEY STICKS then the standard deviation would be 3 HOCKEY STICKS Standard Deviation
  • 43. Standard Deviation The standard Deviation is used in many statistical formulas and analyses.
  • 44. Standard Deviation The standard Deviation is used in many statistical formulas and analyses. Here is the formula: Standard Deviation
  • 45. Standard Deviation The standard Deviation is used in many statistical formulas and analyses. Here is the formula: Standard Deviation
  • 47. Standard Deviation Person Score A 1 B 4 C 7 Standard Deviation
  • 48. Standard Deviation Person Score A 1 B 4 C 7 Standard Deviation
  • 49. Standard Deviation Person Score A 1 B 4 C 7 Standard Deviation
  • 50. Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Standard Deviation
  • 51. Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Standard Deviation
  • 52. Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Standard Deviation
  • 53. Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Standard Deviation
  • 54. Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9
  • 55. Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Standard Deviation
  • 56. Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Standard Deviation
  • 57. Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Standard Deviation
  • 58. Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Standard Deviation
  • 59. Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Square Root 2.4 Standard Deviation
  • 60. Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Square Root 2.4 Standard Deviation
  • 61. Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Square Root 2.4 This is the Standard Deviation Standard Deviation
  • 62. Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Square Root 2.4 So, technically, the standard deviation is the root average squared deviation from the mean. Standard Deviation
  • 63. Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Square Root 2.4 So, technically, the standard deviation is the root average squared deviation from the mean. Standard Deviation
  • 64. Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Square Root 2.4 So, technically, the standard deviation is the root average squared deviation from the mean. Standard Deviation
  • 65. Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Square Root 2.4 So, technically, the standard deviation is the root average squared deviation from the mean. Standard Deviation
  • 66. Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Square Root 2.4 So, technically, the standard deviation is the root average squared deviation from the mean. Standard Deviation
  • 67. Standard Deviation Person Score A 1 B 4 C 7 Mean 4 Score - Mean 1 โ€“ 4 4 โ€“ 4 7 โ€“ 4 Deviation = -3 = 0 = +3 Squared -32 = 9 02 = 0 +32 = 9 Sum 18 Average 6 Square Root 2.4 So, technically, the standard deviation is the root average squared deviation from the mean. Standard Deviation
  • 68. Standard Deviation The standard deviation has many uses. Standard Deviation
  • 69. Standard Deviation The standard deviation has many uses. First and foremost it is a number that describes how scores in a distribution are spread out from one another. Standard Deviation
  • 70. Standard Deviation The standard deviation has many uses. First and foremost it is a number that describes how scores in a distribution are spread out from one another. Standard Deviation = 2 Standard Deviation
  • 71. Standard Deviation The standard deviation has many uses. First and foremost it is a number that describes how scores in a distribution are spread out from one another. Standard Deviation = 2 Standard Deviation = 18 Standard Deviation
  • 72. Standard Deviation The standard deviation has many uses. First and foremost it is a number that describes how scores in a distribution are spread out from one another. Standard Deviation = 2 Standard Deviation = 18 What do you think a distribution with a standard deviation of 1 might look like? Standard Deviation
  • 73. Standard Deviation The standard deviation has many uses. First and foremost it is a number that describes how scores in a distribution are spread out from one another. Standard Deviation = 2 Standard Deviation = 18 What about standard deviations of 10 or 20? Standard Deviation

Editor's Notes

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  3. Make that change throughout
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